Transceiver device and method of processing signals

ABSTRACT

A method of processing signals may include calculating a covariance matrix and a correlation vector based on an input signal vector and an output signal vector; identifying a plurality of critical elements of a parameter vector based on a predefined criteria, wherein the parameter vector describes a relationship between the input signal vector and the output signal vector; calculating a solution to a linear system to generate a reduced parameter update vector having a plurality of elements, wherein the linear system is based on the plurality of critical elements of the parameter vector, the covariance matrix, and the correlation vector; updating the plurality of critical elements of the parameter vector using the reduced parameter update vector to generate an updated parameter vector, wherein the reduced parameter update vector has less elements than the parameter vector; and processing one or more signals associated with the input signal vector using the updated parameter vector.

TECHNICAL FIELD

Various embodiments relate generally to a transceiver device and amethod of processing signals.

BACKGROUND

Many conventional wireless devices perform both wireless transmissionand reception and therefore contain both transmitter and receivercomponents (i.e. transceivers). Transceiver designs may include suchtransmitter and receiver components arranged in close proximity another,and there often may exist a level of indirect or shared coupling betweenthe components. As a result, many transceiver designs may be susceptibleto leakage between the transmitter and receiver chains.

Leakage may be especially prevalent in single or shared antenna systems,where the transmitter and receiver chains may both be coupled toduplexing circuitry. Accordingly, leakage from the transmitter chain tothe receiver chain may result in self-interference, where a signalintended for transmission is imposed onto a received signal.

As the transmitted signal is known at the transceiver, it may bepossible to model the path between the transmitter and receiver chainsin order to cancel out the leakage signal from the signal at thereceiver.

BRIEF DESCRIPTION OF THE DRAWINGS

In the drawings, like reference characters generally refer to the sameparts throughout the different views. The drawings are not necessarilyto scale, emphasis instead generally being placed upon illustrating theprinciples of the invention. In the following description, variousembodiments of the invention are described with reference to thefollowing drawings, in which:

FIG. 1 shows a block diagram corresponding to a mobile device;

FIG. 2 shows a flow diagram illustrating a selective optimizationprocess;

FIG. 3 shows a block diagram illustrating internal components of acommunication terminal; and

FIG. 4 shows a flow diagram illustrating a method of processing signals.

DESCRIPTION

The following detailed description refers to the accompanying drawingsthat show, by way of illustration, specific details and embodiments inwhich the invention may be practiced.

The word “exemplary” is used herein to mean “serving as an example,instance, or illustration”. Any embodiment or design described herein as“exemplary” is not necessarily to be construed as preferred oradvantageous over other embodiments or designs.

The words “plural” and “multiple” in the description and the claims, ifany, are used to expressly refer to a quantity greater than one.Accordingly, any phrases explicitly invoking the aforementioned words(e.g. “a plurality of [objects]”, “multiple [objects]”) referring to aquantity of objects is intended to expressly refer more than one of thesaid objects. The terms “group”, “set”, “collection”, “series”,“sequence”, “grouping”, “selection”, etc., and the like in thedescription and in the claims, if any, are used to refer to a quantityequal to or greater than one, i.e. one or more. Accordingly, the phrases“a group of [objects]”, “a set of [objects]”, “a collection of[objects]”, “a series of [objects]”, “a sequence of [objects]”, “agrouping of [objects]”, “a selection of [objects]”, “[object] group”,“[object] set”, “[object] collection”, “[object] series”, “[object]sequence”, “[object] grouping”, “[object] selection”, etc., used hereinin relation to a quantity of objects is intended to refer to a quantityof one or more of said objects. It is appreciated that unless directlyreferred to with an explicitly stated plural quantity (e.g. “two[objects]” “three of the [objects]”, “ten or more [objects]”, “at leastfour [objects]”, etc.) or express use of the words “plural”, “multiple”,or similar phrases, references to quantities of objects are intended torefer to one or more of said objects.

It is appreciated that any vector and/or matrix notation utilized hereinis exemplary in nature and is employed solely for purposes ofexplanation. Accordingly, it is understood that the approaches detailedin this disclosure are not limited to being implemented solely usingvectors and/or matrices, and that the associated processes andcomputations may be equivalently performed with respect to sets,sequences, groups, etc., of data, observations, information, signals,etc.

Furthermore, it is appreciated that references to a “vector” may referto a vector of any size or orientation, i.e. including a 1×1 vector(e.g. a scalar), a 1×M vector (e.g. a row vector), and an M×1 vector(e.g. a column vector). Similarly, it is appreciated that references toa “matrix” may refer to matrix of any size or orientation, i.e.including a 1×1 matrix (e.g. a scalar), a 1×M matrix (e.g. a rowvector), and an M×1 matrix (e.g. a column vector).

As used herein, a “circuit” may be understood as any kind of a logicimplementing entity, which may be special purpose circuitry or aprocessor executing software stored in a memory, firmware, or anycombination thereof. Furthermore, a “circuit” may be a hard-wired logiccircuit or a programmable logic circuit such as a programmableprocessor, for example a microprocessor (for example a ComplexInstruction Set Computer (CISC) processor or a Reduced Instruction SetComputer (RISC) processor). A “circuit” may also be a processorexecuting software, for example any kind of computer program, forexample a computer program using a virtual machine code such as forexample Java. Any other kind of implementation of the respectivefunctions which will be described in more detail below may also beunderstood as a “circuit”. It may also be understood that any two (ormore) of the described circuits may be combined into one circuit.

The term “base station” used in reference to an access point of a mobilecommunication network may be understood as a macro base station, microbase station, Node B, evolved NodeBs (eNB), Home eNodeB, Remote RadioHead (RRHs), relay point, etc.

As used herein, a “cell” in the context of telecommunications may beunderstood as a sector served by a base station. Accordingly, a cell maybe a set of geographically co-located antennas that correspond to aparticular sectorization of a base station. A base station may thusserve one or more “cells” (or sectors), where each cell is characterizedby a distinct communication channel.

FIG. 1 shows a block diagram illustrating the internal components of amobile device 100. Mobile device 100 may be e.g. a mobile terminaldevice configured to perform wireless communications over a radio accessnetwork. For example, mobile device 100 may be configured to operateaccording to a 3^(rd) Generation Partnership Project (3GPP) wirelessnetwork, such as e.g. a Global System for Mobile Communications (GSM)network, Universal Mobile Telecommunications System (UMTS) network, orLong Term Evolution (LTE) network. Mobile device 100 may be furtherconfigured to operate according to a number of other radio accesstechnologies, and it is thus appreciated that the disclosure detailedherein may be applied to any number of different radio accesstechnologies.

Mobile device 100 may include antenna 102, duplexer 104, receiver (RX)chain 106, transmitter (TX) chain 108, modeling logic 110, cancelationlogic 112, and parameter estimation logic 114. As shown in FIG. 1,antenna 102 may be shared between RX chain 106 and TX chain 108 in orderto perform both wireless reception and transmission. Although antenna102 is illustrated as a single antenna, it is appreciated that antenna102 may be similarly implemented as an antenna array including aplurality of antennas.

The aforementioned components and logic circuitry of mobile device 100may be implemented as separate hardware components or separate circuits,e.g. as separate integrated circuits, as illustrated in FIG. 1. However,it is understood that some or all of the circuits may be implemented bya common programmable processor, such as e.g. a microprocessor.Accordingly, some or all of the functionality of the one or more of theaforementioned components may be consolidated into a single hardwarecomponent. It is also understood that mobile device 100 may include anumber of additional components, including hardware, processors, memory,and other specialty or generic hardware/processors/circuits, etc., inorder to support a variety of additional operations of wireless radiocommunications. Mobile device 100 may additionally include corehardware, such as one or more processors dedicated to performing and/orsupport mobile communication applications. Mobile device 100 may alsoinclude a variety of user input/output devices such as displays,keypads, touchscreens, speakers, external buttons, etc.

Duplexer 104 may be utilized in order to facilitate both wirelessreception by RX chain 106 and wireless transmission by TX chain 108using antenna 102. For example, antenna 102 may wirelessly receive oneor more downlink signals and provide resulting a resulting downlinksignal to duplexer 104. Duplexer 104 may provide the downlink signal toRX chain 106. RX chain 106 may process the downlink signal, such as witha low noise amplifier (LNA), automatic gain controller (AGC), and downconverter/analog-to-digital converter (ADC), and may output resultingsignal y(t).

TX chain 108 may provide an uplink signal to duplexer 104, which maythen provide the uplink signal to antenna 102 for wireless transmission.For example, TX chain may receive signal X(t) intended for uplinktransmission and perform transmission processing and amplificationthereon, such as with processing circuity and a power amplifier. TXchain 108 may then provide the resulting signal to duplexer 104 forsubsequent wireless transmission by antenna 102. It is appreciated thatX(t) may be e.g. a singular value or a grouping of a plurality ofsingular values, such as e.g. a transmission symbol representing aplurality of binary bits.

Accordingly, both RX chain 106 and TX chain 108 may share a commonconnection to duplexer 104 in order to receive downlink signals andtransmit uplink signals, respectively. Due to imperfect isolation, theuplink signal provided by TX chain 108 may leak into RX chain 106,thereby potentially corrupting the received signal produced by RX chain106. As shown in FIG. 1, RX chain 106 may output signal y(t), wherey(t)=y₁(t)+y_(DL)(t), y₁(t) is the leakage signal corresponding to X(t),and y_(DL)(t) is the received downlink signal corresponding to thedesired downlink signal receiver by antenna 102. It is appreciated thatadditional leakage paths between TX chain 108 and RX chain 106 mayexist.

y(t) as output by RX chain 106 may therefore contain two distinctcomponents in y_(DL)(t) and y₁(t), where y_(DL)(t) corresponds to thereceived downlink signal containing desired information and y₁(t)corresponding to signal X(t) leaking from TX chain 108. y(t) may thus becorrupted by the presence of y₁(t).

The presence of leakage y₁(t), also known as “self-interference”, maycause significant performance degradation at the receiver side. It isappreciated that leakage such as y₁(t) may be capable of causing suchself-interference even in frequency duplexing systems that utilizeseparate transmission and reception frequency bands or time duplexingsystems that transmit and receive during separate time periods. Theunderlying self-interference problem is similarly not solved by the useof dedicated (i.e. non-shared) antennas, as leakage may still occurthrough a variety of indirect coupling paths between the RX and TXchain.

Self-interference caused by TX chain leakage may be addressed byestimating the leakage at the signal produced by the RX chain (i.e.y₁(t) in y(t)) and canceling the estimated leakage. As the leakagesource signal X(t) is known at mobile device 100, it may thus bepossible to model the path from TX chain 108 to RX chain 106 in order toestimate y₁(t) from x(t), thereby obtaining leakage estimate ŷ₁(t). Aparametrized linear model may be used to model the relationship betweenX(t) and y₁(t). Based on the output of the model, the leakage signaly₁(t) may be canceled out of the RX chain signal y(t) through the use ofleakage estimate ŷ₁(t).

As shown in FIG. 1, TX chain input signal X(t) may be provided tomodeling logic 110. Modeling logic 110 may output leakage estimate ŷ₁(t)to cancelation logic 112, which may then cancel out leakage from RXchain input signal y(t) based on the provided leakage estimate ŷ₁(t).Modeling logic 110 may determine leakage estimate ŷ₁(t) by utilizing aparameter vector W to model the relationship between input signal X(t)and leakage signal y₁(t). Parameter estimation logic 114 maycontinuously update the model parameters of parameter vector W ofmodeling logic 110 in order to provide accurate model characterizationin real-time, thereby enabling mobile device 100 to obtain an accurateestimate ŷ₁(t) of leakage signal y₁(t).

Modeling logic 110 may model the relationship between X(t) and y₁(t) toproduce leakage estimate ŷ₁(t) using parameter vector W as follows:

ŷ ₁(t)=W′φ(X(t))  (1),

where W′ is the transpose of W and φ(X(t)) is a function of the currentand past input samples contained in RX chain input signal vectorX(t)={X(t), X(t−1), . . . X(t−T₀)} with T₀ being the memory length ofthe model. As previously detailed, X(t) may represent a singular valueor may be a grouping of a plurality of singular values, such as atransmission symbol.

The function φ may be a “kernelization” or “mapping” function, and maybe utilized in order to compensate for the non-linear relationshipbetween y₁(t) and TX chain input signals X(t). This non-linearity may beintroduced into the leakage path from TX chain 108 to RX chain 108 dueto any of a number of sources, such as differing transmission andreception frequency bands, non-linear components such as poweramplifiers, and a number of additional components such as filters anddelays. As a result, leakage signal y₁(t) may be a non-linear functionof current and past TX chain input signals X(t):=(X(t), X(t−1), . . . ,X(t−T₀)).

Kernelization function φ(X(t)) may thus be used to translate original(i.e. unmapped) input signals X(t), X(t−1), . . . , X(t−T₀) into thelinear space corresponding to leakage signal y₁(t). A parametrizedlinear model based on the estimation of parameter vector W may then beutilized in order to estimate leakage estimate ŷ₁(t) from X(t) based onEquation 1.

Accordingly, a solution to the self-interference cancelation problem maybe provided through linear parameter estimation of the parameter vectorW. Maintenance of a parameter vector W that accurately characterizes therelationship between TX chain input signals X(t) and leakage signaly₁(t), thereby providing an effective means of estimating leakageestimate ŷ₁(t). As the relationship between X(t) and y₁(t) is complex,parameter vector W may contain hundreds of parameters. W must beconstantly updated based on observations of TX chain input signals X(t)and RX chain input signals Y(t) in order to maintain a sufficientlycomprehensive model.

Classical methods such as linear mean square (LMS) and recursive linearsquare (RLS) may be utilized in order to estimate parameter vector Wfollowing translation of X(t) into the linear domain of y₁(t) withkernelization function φ(X(t)). However, these classical methods maysuffer from a variety of concerns relate to convergence speed,complexity, and power consumption requirements of these classicalmethods. LMS offers a simple implementation (i.e. relatively lowcomplexity) but suffers from slow convergence speeds. In contrast, RLSprovides fast convergence speeds but proves too complex for manyreal-time implementations.

Several simplifications have been offered for RLS approaches in order toreduce complexity to practical levels. However, these simplificationsface several drawbacks in dynamic scenarios such as the proposedscenario of self-interference cancelation. Methods offering largereductions in complexity often prove to be too simple to avoid spikes inthe estimation and/or cancelation, while more comprehensive methodssuffer from over-complication and require precise offline parametersetting.

For example, coordinate descent (CD) offers a drastic reduction incomplexity over the aforementioned classical methods. As opposed toupdating every parameter in W, CD algorithms update only a singleparameter. While this approach provides a predictable decrease incomplexity, convergence speed may be unacceptably slow.

Another proposed simplification to the classical approaches is conjugategradient (CG), where each parameter update to W is based on a quadraticcost function and descends along an optimal direction with optimalstep-size determined based on the assumption of a linear system. Due tothe optimized update directionality, CG may offer fast convergence in avariety of implementations. However, in many cases the overallcomplexity will be similar to RLS.

Accordingly, reception of wireless signals by mobile device 100 may beimproved through the implementation of a parameter update scheme forparameter vector W for use in estimating leakage signal y₁(t) thatoffers high accuracy, relatively fast convergence speed, and reducedcomplexity.

Updates of W may be necessary given each new observation of TX chaininput signals X(t) and RX chain input signals Y(t). As previouslydetailed, the relationship modeling the estimated leakage ŷ₁(t) from TXchain input signal X(t) may be denoted as ŷ₁(t)=W′(X(t)) (see Equation1), where φ(X(t)) is an N×1 vector mapping current and past TX chaininput signals X(t):=(X(t), X(t−1), . . . , X(t−T₀)) to the linear domainof ŷ₁(t). Each element of φ may be a non-linear function of one or morepast TX chain input signals of X(t). Each new observation of X(t) (i.e.each subsequent transmitted TX chain input signal) may therefore requirean update of vector φ(X(t)), as one or more elements of φ(X(t)) maydepend on the most recently transmitted TX chain signal X(t).

For clarity, u(t) may be used to denote φ(X(t)). At a given time t,Equation 1 may be expressed as follows:

u(t)^(′)W = y₁(t) u(t − 1)^(′)W = y₁(t − 1) … u(1)^(′)W = y₁(1)

This may be written into compact form using the matrices U(t) and Y₁(t)as follows:

U(t)′W=Y ₁(t)  (2),

where U(t):=(u(t), . . . , u(1)) and Y₁(t):=(y₁(t), . . . , y₁(t))′.

The parameter vector W that achieves the minimum mean square error(MMSE) is typically the optimal solution. It may be shown that thevector W achieving the MMSE is additionally the solution to Equation (3)as follows:

U(t)U(t)′W=U(t)Y ₁(t)  (3).

R(t) may then be defined as R(t):=U(t)U(t)′=u(t)u(t)′+u(t−1)u(t−1)′+ . .. +u(1)u(1)′, which is the empirical covariance matrix of the kernelizedinput signal vectors (α(X(k)), k=1, 2, . . . t) where vectorX(k)=(X(k),X(k+1), . . . , X(k−T₀)). Similarly, β(t) may be defined asβ(t)=U(t)Y₁(t), which is the correlation between the kernelized inputsignal vectors φ(X(k)) and the observation vector Y₁.

Equation (3) may then be rewritten using R(t) and β(t):

R(t)W=β(t)  (4).

Accordingly, Equation (4) may be solved for W in order to obtain aparameter vector W that accurately models the relationship betweenφ(X(t)) and y₁(t), thereby providing a model to estimate the leakageŷ₁(t) in order to effectively cancel the leakage from RX chain inputsignal y(t). W may consequently used in the estimation and cancelationof leakage in future transmissions.

A potential solution for W in Equation (4) may be realized by computingthe inverse of R(t). However, R(t) have dimensions greater than 100×100,which consequently presents an increasingly complex inversion operation.The aforementioned parameter estimation approaches such as LMS, RLS, CD,and CG have thus been offered as alternatives providing reducedcomplexity.

For example, CG may be utilized in order to compute W satisfyingEquation (4) that involves updating each element of W based on aquadratic cost function and optimal step-size. However, this approachmay be overly complex as W will often have dimensions greater than100×1, and accordingly will require an equivalent number of updates inorder to complete CG estimation thereof.

CD, as previously detailed, involves only the update of a single elementof W. However, the drastic reduction in complexity may lead to increasedsusceptibility to spikes in the estimation and/or cancelation of leakageonce the solution is applied.

FIG. 2 details a flow chart illustrating method 200 for performing anupdate of parameter vector W. It is appreciated that while method 200will be described in relation to estimating leakage in aself-interference cancelation application, the methods andimplementations detailed herein may be utilized in a variety ofdifferent applications. For example, it is appreciated that suchapproaches may be applied to any number of systems requiring similarlinear estimation problems. Method 200 may thus be applied as analternative to a number of LMS, RLS, CD, or CD parameter estimationapproaches.

Method 200 may begin with a system such as in Equation 4. In aself-interference cancelation, method 200 may aim to find a parametervector W to accurately estimate the relationship between kernelizedinput signal vector φ(X(t)) and leakage y₁(t), such as detailedregarding FIG. 1. Accordingly, an appropriate W for the systemy₁(t)=W′φ(X(t)) may be obtained by finding a solution W(t) that resolvesthe system R(t)W(t)=β(t), where R(t) is the covariance matrix ofkernelized RX chain input signal vector φ(X(t)) and β(t) is thecorrelation between between the kernelized TX chain input signal vectorφ(X(t)) and RX chain input signal vector Y₁(t).

Method 200 may be implemented as an iterative algorithm, and may performcontinuous updates to parameter vector W based on new observations. Forexample, method 200 may receive new observations for X(t) and Y(t)during each iteration, and may subsequently perform an update onparameter vector W based on the new observations during each iteration.

Method 200 may therefore begin at time t with past values R(t−1),β(t−1), and W(t−1), i.e. with the values for R, β, and W from theprevious iteration of method 200. At 202, method 200 may obtain newobservations X(t) and y(t). For example, method 200 may observe the nextTX signal scheduled for transmission over TX chain 108, i.e. X(t).Method 200 may then update input signal vector X(t) to include the nextTX signal X(t), and subsequently update kernelized input signal vectorφ(X(t)). Method 200 may also receive observation y(t) and updateobservation vector Y(t).

Accordingly, method 200 may update covariance matrix R(t) andcorrelation vector β(t) in 204, i.e. by applying the newest observationsx(t) (in the form of φ(X(t))) and y(t) to R(t−1) and β(t−1).Accordingly, method 200 must determine an appropriate updated W(t) basedon W(t−1), R(t), and β(t). Method 200 may therefore seek to obtain anaccurate current W(t) in order to apply W(t) to the linear relationshipŷ₁(t)=W′φ(X(t)), thereby enabling generation of leakage estimate ŷ₁(t)for use in self-interference cancelation.

As opposed to updating every element in W, method 200 may instead selecta subset of elements in W to update. In other words, method 200 mayidentify a plurality of critical elements of W to update. Method 200 maythen determine and apply an appropriate update for each of the criticalelements of W. Method 200 may determine an update vector δW during eachiteration thereof and update W at time t as W(t)=W(t−1)+δW. Updatevector δW may be non-zero at only D positions, and consequently only Dpositions of W may be updated during each iteration of method 200.Accordingly, a total of D critical elements of W may be updated duringeach iteration of method 200. The parameter D may be selected accordingto system dynamics, such as e.g. D=2, 4, 6, etc. Larger values of D mayrequire increased complexity due to the increase in the number ofelements of W to be updated but may improve accuracy. In contrast,smaller values of D may reduce complexity but similarly reduce accuracy,thereby leaving the self-interference cancelation susceptible to spikes.

Accordingly, method 200 may aim to identify D critical elements of W toupdate. D may therefore be a predefined quantity determining thequantity of critical elements of W to be updated. In order to identifythe D critical elements of W, 204 may determine a “remainder” vectorr(t) as r(t)=R(t)W(t−1)−β(t). Remainder vector r(t) may thus havedimension N×1 correspondent to the dimensions of R(t) (N×N), β(t) (N×1),and W (N×1).

After determining remainder vector r(t), 206 may rank the N entries ofr(t) according to a predefined criteria. The predefined criteria may bee.g. magnitude, and accordingly each element of r(t) may be rankedaccording to the absolute value of each element. It is appreciated thata number of different ranking criteria may be utilized to identify thehighest-ranked elements of r(t).

After ranking the elements of r(t), 208 may select the entries of r(t)corresponding to the highest-ranked D elements. In other words, 208 mayselect the D entries of r(t) with the largest magnitudes in animplementation where the predefined criteria is magnitude.

The entries of W(t−1) corresponding to the the highest-ranked D elementsof r(t) may thus be selected to be updated, i.e. the entries of W(t−1)corresponding to the highest ranked D elements of r(t) may be identifiedas the critical elements of W. It is appreciated that 206 and 208 mayfunction to identify the critical elements of W(t−1), i.e. the elementsof W(t−1) that have the largest need for update. Accordingly, thecritical elements of W(t−1) may be selected for update to arrive at W(t)while less-essential elements of W(t−1) may not be updated. Method 200may thus reduce the overall complexity involved in the update processfor W while ensuring that necessary updates are completed.

After identifying the D critical elements of W based on remainder vectorr(t), method 200 may proceed to compute the corresponding updatesthereof. As previously detailed, method 200 may update W from W(t−1) tocurrent W(t) by computing update vector δW, and subsequently calculatingW(t) as W(t)=W(t−1)+δW. Update vector δW having D non-zero entries maytherefore be obtained to coincide with the D critical elements of W tobe updated.

210 may thus determine the corresponding D×D sub-matrix R_(D)(t) fromR(t) and the corresponding D×1 sub-vector r_(D)(t) from r(t) based onthe D critical entries of r(t) identified in 208. Specifically, ifpositions (j₁, j₂, . . . , j_(D)) are selected as critical in r(t) toyield r_(D)(t), R_(D)(t) will then consist of the entries {(a, b), wherea and b are in (j₁, j₂, . . . , j_(D))} in R(t).

Accordingly, 210 may yield R_(D)(t) and r_(D)(t). 212 may then apply thedetermined sub-matrix R_(D)(t) and sub-vector r_(D)(t) to produce a newsystem of reduced dimensions as follows:

R _(D)(t)δW _(D) =r _(D)(t)  (5),

where δW_(D) is a D×1 unknown vector. It is appreciated that each of theD elements of δW_(D) corresponds to one of the D critical entries ofW(t).

212 may then solve the equation system of Equation 5 for δW_(D), such asby using a linear estimation algorithm. As the elements of Equation 5are considered substantially linear, any number of linear estimationapproaches may be applied in order to determine an effective solution toEquation 5. For example, the aforementioned CG algorithm may be appliedto the D-dimensional system of Equation 5. While CG may proveexcessively complex for the 100+-dimension system R(t)W=β(t), the systemof Equation 5 with a suitably chosen D, such as e.g. 2, 4, 6, etc., maybe comparably manageable. As the optimization is being applied to asubstantially smaller system, method 200 may offer a large reduction incomplexity as compared to optimization algorithms operating on thefull-dimensioned system R(t)W=β(t). It is appreciated that any number ofalternate optimization algorithms may be similarly applied, such as anyof a variety of linear estimation methods including CD, RLS, LMS, etc.

The application of CG to Equation 5 in 212 may consequently determine asolution δW_(D), where the solution δW_(D) is understood to be anapproximate solution of the linear system of Equation 5. 214 may thenmap the D total entries of δW_(D) to the corresponding D criticalentries of δW. Specifically, δW may be initially defined as δW=0_(Nx1).The entries of δW may then be populated as δW(j_(k))=δW_(D)(k), k=1, . .. , D, thereby mapping the D entries of δW_(D) to δW. Accordingly, theremaining N−D entries of δW_(D) will be set to zero, as these entrieswere not selected by 208 as critical entries of W according to theranking criteria applied to remainder vector r(t).

216 may then perform the update of parameter vector W as W(t)=W(t−1)+δWusing update vector δW obtained in 214. Accordingly, D elements of W maybe updated in a single iteration of method 200, i.e. with anoptimization algorithm such as CG, where the D elements have beenidentified as being critical entries with a crucial need for update. AsCG is only applied to a D-dimensional system, complexity issubstantially reduced. However, critical entries of W may still beupdated upon each observation, thereby retaining a high degree ofaccuracy in the updates of parameter vector W.

Method 200 may then apply updated W in order to estimate the leakage forself-interference cancelation according to Equation 6:

ŷ ₁(t+1)=φ(X(t+1))′W(t)  (6),

where ŷ₁ (t+1) is the leakage estimate corresponding to the nexttransmit symbol X(t+1) to be transmitted over TX chain 108, φ(X(t+1)) isthe updated kernelized input signal vector based on new observationX(t+1), and W(t) is the updated parameter vector W as determined in 216.

The leakage estimate ŷ₁ (t+1) may then be utilized in order to cancelout the leakage originating TX chain 108 due to the subsequenttransmission of TX signal X(t+1) from received signal X(t). Accordingly,the leakage signal y₁(t+1) may be substantially canceled orsignificantly reduced from received signal y(t), thereby allowing forreception of cleaned signal substantially composed of desired downlinksignal y_(DL)(t+1).

As shown in FIG. 2, method 200 may be implemented as an iterativeprocess, and may continuously repeat at times t+1, t+2, . . . , in orderto continuously reduce self-interference in a mobile device.Accordingly, D positions of W may be selected during each iteration andsubsequently updated using a reduced D-dimensional system, as previouslydescribed. It is appreciated that the D critical entries of W selectedfor update will likely vary for each iteration according to the rankingand selection performed by 206 and 208.

While the each iteration of method 200 may utilize a complexoptimization algorithm such as CG to compute update vector δW_(D), thecomplexity may remain manageable due to the reduced dimensions of theapplied system. Accordingly, method 200 may be easily integrated into avariety of devices, such as conventional smart phones, tablets, andother mobile devices.

It is appreciated that the parameter D may be dynamic, and accordinglymay be adaptable. For example, a mobile device such as mobile device 100implementing the above-detailed selective optimization processes may beconfigured to measure a reception characteristic, such by periodicallymeasuring the signal-to-noise ratio or analyzing an error correctionrate based on received signal y(t). Mobile device 100 may then determinethat reception quality is substantially poor, and accordingly mayincrease the value of D to a higher value in order to potentially obtaina more accurate leakage estimate ŷ₁(t) for self-interferencecancelation. Alternatively, mobile device 100 may determine thatreception quality is substantially high, and accordingly may reduce thevalue of D in order to further reduce processing requirements involvedin the optimization algorithm processing. Method 200 may thus bemodified to include such an analysis of reception quality and acorresponding update to D, if necessary.

FIG. 3 shows communication terminal 300. Communication terminal 300 mayinclude at least antenna 302, transceiver 304 including transmit chain306 and receive chain 308, processing circuit 310, core CentralProcessing Unit (CPU) 312, memory 314, and user input/output 316.

Communication terminal 300 may transmit and receive wireless signalsusing antenna 302 and transceiver 304. Specifically, transmit chain 306and receive chain 308 of transceiver 304 may utilize antenna 302 totransmit signals from communication terminal 300 and receive signals atcommunication terminal 300, respectively, such as by utilizing duplexingcircuitry. It is appreciated that antenna 302 may be a single antenna ormay be an antenna array composed of a plurality of antennas.

Communication terminal 300 may be configured to perform wirelesscommunications according to any of a number of different radio accesstechnologies. For example, communication terminal 300 may be configuredto perform wireless communications according to a cellularcommunications protocol, such as a 3GPP wireless network e.g. GSM, UMTS,or LTE. Communication terminal 300 may additionally or alternatively beconfigured to perform wireless communications according to short rangecommunications protocol, such as WiFi or Bluetooth.

Core CPU 312 may be utilized to support core functionality ofcommunication terminal 300, such as by supporting one or more radioaccess technologies. Core CPU 312 may thus be configured to execute aprotocol stack according to the one or more supported radio accesstechnologies. Core CPU 312 may include audio processing circuits, suchas audio encoding and/or audio decoding circuits. Core CPU 312 may act acontroller, and may be configured to control one or more of theadditional components of communication terminal 300. Core CPU 312 may beimplemented as e.g. a microprocessor or any other type of programmablelogic. In an exemplary aspect of the disclosure, processing 310 may beincorporated as part of core CPU 312.

As shown in FIG. 3, communication terminal 300 may further includememory 314. Memory 314 may be composed of e.g. a read only memory (ROM)and/or a random access memory (RAM). Memory 314 additionally may becomposed of several separately implemented memory components, and may beavailable for use by one or more further components of communicationterminal 300. Memory 314 may additionally store one or more sets ofprogram code, such as program code utilized to control core CPU 312and/or processing circuit 310. Memory 314 may additionally be utilizedto store wireless communication data, such as data received by receivechain 308 and/or data intended for transmission by transmit chain 306.

Communication terminal 314 may additionally include components tointeract with a user, such as user input/output 316. User input/output316 may include one or more input and/or output devices, such askeypads, physical buttons, displays, touch sensitive displays,loudspeakers, microphones, cameras, etc.

The internal components of communication terminal 300 may be coupledwith one another via one or more lines, such as e.g. one or more databuses. Accordingly, one or more of the internal components ofcommunication terminal 300 may interact with one another by exchangingdata therewith. The exchange of data within the internal components ofcommunication terminal 300 may be controlled by e.g. core CPU 312.

Similarly to mobile device 100, as communication terminal 300 mayinclude transceiver components (transceiver 304), communication terminal300 may be susceptible to leakage from transmit chain 306 to receivechain 308. Accordingly, communication terminal 300 may be configured tomitigate and/or cancel transmit chain leakage from signals received byreceive chain 308.

Communication terminal 300 may therefore be configured to generate anestimated leakage signal based on a signal intended for transmissionover transmit chain 306. Communication terminal 308 may then utilize theestimated leakage signal to mitigate and/or cancel an actual leakagesignal from a signal received by receive chain 308.

Communication terminal 300 may therefore be provided with processingcircuit 310, which may interact with transmit chain 306 and receivechain 308 in order to mitigate and/or cancel leakage from signalsreceived by receive chain 308.

Transmit chain 306 may therefore be configured to transmit one or moretransmit signals. Receive chain 308 may be configured to receive one ormore receive signals.

Processing circuit 310 may be configured to implement selectiveoptimization of a parameter vector estimating the leakage betweentransmit chain 306 and receive chain 308, such as the selectiveoptimization process of method 200. Specifically, processing circuit 310may be configured to calculate a covariance matrix based on the one ormore transmit signals and the one or more receive signals. Specifically,processing circuit 310 may be configured to first identify a transmitsignal vector including one or more of the transmit signals. Processingcircuit 310 may then apply a kernelization function on one or more ofthe transmit signals in the transmit signal vector to generate akernelized transmit signal vector. Processing circuit 310 may thencalculate the covariance matrix as the covariance matrix of thekernelized transmit signal vector.

Processing circuit 310 may also identify a receive signal vectorincluding one or more of the receive signals. Processing circuit 310 maythen generate a correlation vector between the kernelized transmitsignal vector and the receive signal vector. Processing circuit 310 maycalculate the correlation vector by determining the correlation betweenthe elements of the kernelized transmit signal vector and the elementsof the receive signal vector.

Processing circuit 310 may continuously calculate a new covariancematrix and a new correlation vector upon obtaining recently transmittedsignals by transmit chain 306 and recently received signals by receivechain 308. In other words, processing circuit 310 may calculate anupdated covariance matrix and an updated correlation vector uponreceiving a new observation from one of or both of transmit chain 306and receive chain 308. Processing circuit 310 may update the kernelizedtransmit signal vector upon obtaining a new transmit signal observationand may update the receive signal vector upon receiving a new receivesignal observation.

In order to approximate the leakage from transmit chain 306 to receivechain 308, processing circuit 310 may determine a parameter vectorrepresenting a relationship between the transmit signal vector and thereceive signal vector, such as the relationship between the transmitsignal vector and a target signal component associated with the receivesignal vector. Processing circuit 310 may determine a parameter vectorthat approximates the linear relationship between the kernelizedtransmit signal vector and signal leakage contained in the receivesignal vector.

Processing circuit 310 may similarly perform continuous updates to theparameter vector over time to reflect new observations from transmitchain 306 and receive chain 308. Processing circuit 310 may update theparameter vector by first updating the covariance matrix and thecorrelation vector based on new observations from transmit chain 306and/or receive chain 308. Processing circuit 310 may then utilize theupdated parameter vector to estimate leakage between transmit chain 306and receive chain 308, and subsequently use the estimated leakage tocancel out actual leakage present in signal received by received chain308.

In order to update the parameter vector to calculate an updatedparameter vector, processing circuit 310 may identify a plurality ofcritical elements of the existing parameter vector to update. In orderto identify the plurality of critical elements, processing circuit 310may calculate a parameter remainder vector based on the existingparameter vector, an updated covariance matrix, and an updatedcorrelation vector. Processing circuit 310 may utilize the covariancematrix and the correlation vector along with the existing parametervector in order to calculate the parameter remainder vector, such as bycalculating the parameter remainder vector as a linear combination ofthe covariance matrix, correlation vector, and existing parametervector.

Processing circuit 310 may then utilize a predefined criteria in orderto evaluate the parameter remainder vector. Processing circuit 310 mayutilized a predefined ranking criteria in order to rank the elements ofthe parameter remainder vector, such as e.g. ranking the elements of theparameter remainder vector based on magnitude. Processing circuit 310may then select a plurality of highest ranked elements, where the numberof highest ranked elements of the plurality of highest ranked elementsis predefined. For example, processing circuit 310 may select an integerquantity of highest ranked elements of the parameter remainder vector asthe plurality of highest ranked elements.

Processing circuit 310 may then identify the plurality of criticalelements of the parameter vector based on the indices of the pluralityof highest ranked elements of the parameter remainder vector. Forexample, processing circuit 310 may select each of the plurality ofcritical elements such that the index of each of the plurality ofcritical elements corresponds to an index of one of the plurality ofhighest ranked elements of the parameter remainder vector. Accordingly,processing circuit 310 may identify the plurality of critical elementsof the parameter vector to be updated.

Processing circuit 310 may then calculate a solution to a linear systemto determine an appropriate update for the parameter vector. The linearsystem may be the linear relationship between the plurality of highestranked elements of the parameter remainder vector and the correspondingelements of the covariance matrix. Processing circuit 310 may thereforegenerate a reduced covariance matrix including the correspondingelements of the covariance matrix. Each of the plurality ofhighest-ranked elements of the parameter remainder vector may correspondto one of the plurality of critical elements of the parameter vector.Processing circuit 310 may solve the linear system using a linearestimation method, such as CG, CD, RLS, LMS, etc. Processing circuit 310may generate a reduced parameter update vector as the solution to thelinear system.

As the linear system has dimensions corresponding to the number ofcritical elements of the plurality of critical elements, the linearsystem has reduced dimensions compared to the dimensions of the originallinear system between the kernelized transmit signal vector and thereceive signal vector. Accordingly, the linear system may requiresubstantially less processing.

Processing circuit 310 may then update the parameter vector using thereduced parameter update vector that was determined as the solution tothe linear system, wherein the reduced parameter update vector has fewerelements than the parameter vector. Processing circuit 310 may updatethe parameter vector by mapping each element of the reduced parameterupdate vector to the corresponding element of the plurality of criticalelements. Processing circuit 310 may e.g. perform element-wise additionof each element of the reduced parameter update vector to thecorresponding critical element of the plurality of critical elements ofthe parameter vector. Processing circuit 310 may obtain an updatedparameter vector.

Processing circuit 310 may then apply the updated parameter vector inorder to cancel signal leakage from receive chain 308. For example,processing circuit 310 may obtain the next transmit signal scheduled fortransmission by transmit chain 308. Processing circuit 310 may thenupdate the kernelized transmit signal vector based on the next transmitsignal, and may then apply the updated parameter vector to the updatedkernelized transmit signal vector, such as e.g. by performing vectormultiplication with the kernelized transmit signal vector with theparameter vector.

Processing circuit 310 may thus obtain an estimated leakage signal.Processing circuit 310 may then receive the next receive signal receivedby receive chain 308, and may utilize the estimated leakage signal tocancel out actual leakage from the next receive signal to produce aclean received signal. Processing circuit 310 may then provide the cleanreceived signal to one or more additional components of communicationterminal 300 for further processing, such as to core CPU 312.

Accordingly, processing circuit 310 may effectively cancel out leakagefrom signals received by receive chain 308. As the linear estimationutilized to approximate the relationship between the transmit signalsand the receive signals is performed on a reduced-dimension system,processing requirements may be substantially reduced. However, properidentification of critical elements of the parameter vector to beupdated may allow processing circuit 310 to accurately approximate thetransmit chain to receive chain leakage relationship, and therebyeffectively mitigate and/or cancel signal leakage.

It is appreciated that communication terminal 300 may include more thanone transceiver, e.g. one or more transceivers in addition totransceiver 304. One or more of the transceivers may be associated witha different radio access technology, and accordingly communicationterminal 300 may be configured to operate according to a plurality ofradio access technologies. It is appreciated that signal leakage asdetailed above may occur between different radio access technologies,such as between a transmit chain of a transceiver for a first radioaccess technology and a receive chain of a transceiver for a secondradio access technology, where the first radio access technology isdifferent than the second radio access technology. Communicationterminal 300 may similarly apply the above-detailed approaches in orderto mitigate and/or cancel any resulting signal leakage, such as byselectively updating a parameter vector that describes the relationshipbetween signal leakage caused by the transceiver for the first radioaccess technology to the transceiver for the second radio accesstechnology.

FIG. 4 shows a flow chart illustrating method 400. Method 400 may be amethod of processing signals according an aspect of this disclosure.

Method 400 may calculate a covariance matrix and a correlation vectorbased on an input signal vector and an output signal vector in 402.Specifically, method 400 may calculate a kernelized input signal vectorby applying a predefined nonlinear mapping function to the input signalvector. Method 400 may calculate the covariance matrix as the covariancematrix of the kernelized input signal vector, and may calculate thecorrelation vector as the correlation vector between the kernelizedinput signal vector and the output signal vector.

Method 400 may then identify a plurality of critical elements of aparameter vector based on a predefined criteria in 404. The parametervector may represent a relationship between the input signal vector andthe output signal vector. Specifically, the parameter vector mayrepresent a linear relationship between the kernelized input signalvector and a target signal component of the output signal vector. In asignal leakage application, the parameter vector may describe the linearrelationship between the kernelized input signal vector and the signalleakage contained in the output signal vector.

Method 400 may calculate a parameter remainder vector as a linearcombination of the parameter vector, the covariance matrix, and thecorrelation vector in order to determine the plurality of criticalelements. Method 400 may then perform an element-wise analysis on theelements of the parameter remainder vector to identify correspondingcritical elements of the parameter vector according to the predefinedcriteria.

For example, the predefined criteria may be based on magnitude. 404 mayaccordingly identify a predefined quantity of elements of the parameterremainder vector that have the largest magnitudes. 404 may then generatea reduced parameter remainder vector based on the predefined quantity ofelements, such as by selecting each of the predefined quantity ofelements to be in the reduced parameter remainder vector.

Method 400 may then utilize the reduced parameter remainder vector tosolve a linear system in order to determine a reduced parameter updatevector in 406, where the reduced parameter update vector has fewerelements than the parameter vector. The reduced parameter vector alsohas a plurality of elements. Method 400 may generate a reducedcovariance matrix by identifying the elements in the covariance matrixthat correspond to the plurality of critical elements in the parametervector, which may accordingly correspond to the elements of the reducedparameter remainder vector.

The linear system may thus include the reduced parameter remaindervector and the reduced covariance matrix. 406 may approximate a solutionto the linear system to generate the reduced parameter update vector,where the reduced parameter update vector is the solution to the linearsystem.

406 may use any linear approximation method to approximate the solutionto the linear system. For example, 406 may utilize CG, CD, LMS, RLS,etc. in order to arrive at a solution to the linear system.

After determining the reduced parameter update vector in 406, method 400may update the plurality of critical elements of the parameter vectorusing the reduced parameter updated vector in 408 to generate an updatedparameter vector, wherein the reduced parameter update vector has lesselements than the parameter vector. 408 may update only the plurality ofcritical elements of the parameter vector to generate the updatedparameter vector, while the remaining elements of the updated parametervector remain unchanged from the parameter vector.

Method 400 may then process one or more signals associated with theinput signal vector using the updated parameter vector in 410. The oneor more signals may originate from the same source as the input signalsof the input signal vector.

For example, the input signal vector may be based on one or moretransmit signals previously transmitted by a transmit chain of atransceiver and the output signal vector may be based on one or morereceive signals previously received by a receive chain of thetransceiver. The parameter vector may describe the relationship betweenthe one or more transmit signals and signal leakage contained in the oneor more receive signals, such as describing a linear relationshipbetween a kernelized input signal vector based on the input signalvector and the signal leakage.

The parameter vector may therefore be utilized in order to estimate thesignal leakage from the transmit chain to the receive chain. Method 400in 410 may therefore apply the parameter vector to the kernelized inputsignal vector to approximate the signal leakage in the one or morereceive signals. 410 may then perform processing to mitigate or cancelthe signal leakage using the signal leakage approximation.

As the linear system operated on in 406 has reduced dimensionscorresponding to the plurality of critical elements, method 400 may beable to utilize less processing power in order to obtain the solution tothe linear system. Accordingly, as opposed to solving a linear system inorder to update every element of the parameter vector, method 400 mayinstead identify only critical elements of the parameter vector andsolve a reduced-dimension linear system in order to perform an update onthese critical elements. It is appreciated that adjusting the predefinedquantity of elements of the parameter remainder vector may determine thedimensions of the linear system, thereby similarly affecting thecomplexity involved in solving the linear system.

It is appreciated that the above-detailed selective optimizationapproaches may be expanded to any number of optimization scenarios. Forexample, while the above disclosure has focused on a self-interferencecancelation approach, it is understood that any number of optimizationapplications may be improved through selective update of a parametervector. For example, the above-detailed selective optimization approachmay be applied to approximate any non-linear equation systemrepresentable in similar form as to Equation 1, where a mapping functionsuch as φ may be used to approximate a linear relationship. Furthermore,the above-detailed selective optimization approach may be additionallyapplied to approximate linear equation systems, such as where the knownparameters are linear and thus no linear mapping function such as φ maybe necessary. Accordingly, it is appreciated that a solution any numberof equation systems may be approximated utilizing the selectiveoptimization approach of this disclosure. Estimation scenarios utilizingCG or CD may be particularly relevant, as the selective optimizationapproach detailed herein may offer reduced complexity over CG whileavoiding problematic spikes associated with CD. Accordingly, selectiveoptimization may be applied in order to provide desirable convergencetime along with robust estimation results.

The following examples pertain to further aspects of the disclosure:

Example 1 is a method of processing signals. The method includescalculating a covariance matrix and a correlation vector based on aninput signal vector and an output signal vector, identifying a pluralityof critical elements of a parameter vector based on a predefinedcriteria, wherein the parameter vector represents a relationship betweenthe input signal vector and the output signal vector, calculating asolution to a linear system to generate a reduced parameter updatevector having a plurality of elements, wherein the linear system isbased on the plurality of critical elements of the parameter vector, thecovariance matrix, and the correlation vector, updating the plurality ofcritical elements of the parameter vector using the reduced parameterupdate vector to generate an updated parameter vector, wherein thereduced parameter update vector has less elements than the parametervector, and processing one or more signals associated with the inputsignal vector using the updated parameter vector.

In Example 2, the subject matter of Example 1 can optionally includewherein the identifying a plurality of critical elements of a parametervector based on a predefined criteria includes selecting a predefinedquantity of elements of the parameter vector as the plurality ofcritical elements.

In Example 3, the subject matter of Example 2 can optionally includewherein the updating the plurality of critical elements of the parametervector using the reduced parameter update vector to generate an updatedparameter vector includes updating only the plurality of criticalelements of the parameter vector.

In Example 4, the subject matter of any one of Examples 1 to 3 canoptionally include further including with a transmit chain of atransceiver, transmitting one or more transmit signals, and with areceive chain of the transceiver, receiving one or more receive signals,wherein the input signal vector is based on the one or more transmitsignals and the output signal vector is based on the one or more receivesignals.

In Example 5, the subject matter of Example 4 can optionally includewherein processing the one or more signals associated with the inputsignal vector using the updated parameter vector includes applying theupdated parameter vector to a new input signal intended for transmissionby the transmit chain of the transceiver to generate an estimatedleakage signal, wherein the estimated leakage approximates signalleakage from the transmit chain to a the receive chain of thetransceiver, and utilizing the estimated leakage signal to cancel anactual leakage signal from a received signal received by the receivechain of the transceiver.

In Example 6, the subject matter of Example 5 can optionally includewherein applying the updated parameter vector to the new input signalintended for transmission by the transmit chain of the transceiver togenerate an estimated leakage signal includes updating the input signalvector based on the new input signal to generate an updated input signalvector, applying a mapping function to the updated input signal vectorto generate a kernelized input signal vector, where the parameter vectordescribes a linear relationship between the kernelized input signalvector and the signal leakage, and applying the updated parameter vectorto the kernelized input signal vector to generate the estimated leakagesignal.

In Example 7, the subject matter of any one of Examples 1 to 6 canoptionally include wherein identifying a plurality of critical elementsof a parameter vector includes identifying a predefined quantity ofelements of a parameter vector as the plurality of critical elements ofthe parameter vector.

In Example 8, the subject matter of any one of Examples 1 to 7 canoptionally include further including applying a predefined mappingfunction to the input signal vector to generate a kernelized inputsignal vector.

In Example 9, the subject matter of Example 8 can optionally includewherein applying a predefined mapping function to the input signalvector to generate a kernelized input signal vector includes applying anon-linear predefined mapping function to the input signal vector,wherein the parameter vector describes a linear relationship between thekernelized input signal vector and a target signal component associatedwith the output signal vector.

In Example 10, the subject matter of Example 9 can optionally includefurther including with a transmit chain of a transceiver, transmittingone or more transmit signals, and with a receive chain of thetransceiver, receiving one or more receive signals, wherein the inputsignal vector is based on one or more transmit signals previouslytransmitted by a transmit chain of a transceiver and the output signalvector is based on one or more receive signals previously received by areceive chain of the transceiver.

In Example 11, the subject matter of Example 10 can optionally includewherein the parameter vector represents a linear relationship betweenthe kernelized input signal vector and signal leakage contained in theone or more receive signals.

In Example 12, the subject matter of Example 8 can optionally includewherein the covariance matrix is the covariance matrix of the kernelizedinput signal vector and the correlation vector is the correlation vectorbetween the kernelized input signal vector and the output signal vector.

In Example 13, the subject matter of any one of Examples 1 to 12 canoptionally include wherein identifying the plurality of criticalelements of the parameter vector based on the predefined criteriaincludes generating a parameter remainder vector by performing a linearoperation on the parameter vector, the covariance matrix, and thecorrelation vector, selecting a predefined quantity of highest-rankedelements of the parameter remainder vector according to the predefinedcriteria, and selecting the elements of the parameter vector that eachcorrespond to a respective highest-ranked element of the predefinedquantity of highest-ranked elements as the plurality of criticalelements of the parameter vector.

In Example 14, the subject matter of Example 13 can optionally includewherein selecting a predefined quantity of highest-ranked elements ofthe parameter remainder vector according to the predefined criteriaincludes selecting a predefined quantity of highest-ranked elements ofthe parameter remainder vector that is less than the quantity ofelements in the parameter vector.

In Example 15, the subject matter of Example 13 can optionally includewherein the predefined criteria is based on magnitude, and whereinselecting the predefined quantity of highest-ranked elements of theparameter remainder vector according to the predefined criteria includesselecting the predefined quantity of elements of the parameter remaindervector having the greatest magnitude as the predefined quantity ofhighest-ranked elements.

In Example 16, the subject matter of Example 13 can optionally includefurther including selecting the predefined quantity of highest-rankedelements of the parameter remainder vector to generate a reducedparameter remainder vector, wherein the reduced parameter remaindervector contains only the predefined quantity of highest-ranked elementsof the parameter remainder vector.

In Example 17, the subject matter of Example 16 can optionally includefurther including selecting the elements of the covariance matrix thatcorrespond to the plurality of critical elements of the parameter vectorto generate a reduced covariance matrix.

In Example 18, the subject matter of Example 17 can optionally includewherein calculating a solution to a linear system to generate a reducedparameter update vector having a plurality of critical elements includescalculating a solution to a linear system that includes the reducedparameter remainder vector and the reduced covariance matrix.

In Example 19, the subject matter of Example 18 can optionally includewherein the linear system describes the linear relationship between thereduced parameter remainder vector and the reduced covariance matrix andwherein calculating the solution to the linear system to generate thereduced parameter update vector includes performing linear approximationto obtain the reduced parameter update vector as the solution to thelinear system.

In Example 20, the subject matter of Example 19 can optionally includewherein performing linear approximation to obtain the reduced parameterupdate vector as the solution to the linear system includes performingconjugate gradient estimation on the linear system.

In Example 21, the subject matter of Example 19 can optionally includewherein updating the plurality of critical elements of the parametervector using the reduced parameter update vector to generate the updatedparameter vector includes updating only the plurality of criticalelements of the parameter vector using the reduced parameter updatevector to generate the updated parameter vector.

In Example 22, the subject matter of any one of Examples 1 to 21 canoptionally include wherein updating the plurality of critical elementsof the parameter vector using the reduced parameter update vector togenerate the updated parameter vector includes updating only theplurality of critical elements of the parameter vector using the reducedparameter update vector to generate the updated parameter vector.

In Example 23, the subject matter of any one of Examples 1 to 22 canoptionally include wherein identifying the plurality of criticalelements of the parameter vector based on the predefined criteriaincludes generating a parameter remainder vector based on the parametervector, the covariance matrix, and the correlation vector, applying thepredefined criteria to the parameter remainder vector to identify aplurality of highest-ranked elements of the parameter remainder vector,and selecting the elements of the parameter vector that each correspondto a respective element of the plurality of highest-ranked elements ofthe parameter remainder vector as the plurality of critical elements ofthe parameter vector.

In Example 24, the subject matter of Example 23 can optionally includewherein the selecting the elements of the parameter vector that eachcorrespond to a respective element of the plurality of highest-rankedelements of the parameter remainder vector as the plurality of criticalelements of the parameter vector includes selecting the plurality ofcritical elements wherein the plurality of critical elements of theparameter vector each have a vector index that corresponds to a vectorindex of a respective highest-ranked element of the plurality ofhighest-ranked elements of the parameter remainder vector.

In Example 25, the subject matter of Example 23 can optionally includewherein the predefined criteria is based on magnitude, and whereinapplying the predefined criteria to the parameter remainder vector toidentify the plurality of highest-ranked elements of the parameterremainder vector includes selecting a predefined quantity of elements ofthe parameter remainder vector that have the highest-magnitudes as theplurality of highest-ranked elements of the parameter remainder vector.

In Example 26, the subject matter of Example 23 can optionally includewherein the linear system describes a linear relationship between thereduced parameter remainder vector and a plurality of elements of thecovariance matrix that correspond with the elements of the reducedparameter remainder vector, and wherein calculating the solution to thelinear system to generate the reduced parameter update vector havingless elements than the parameter vector includes applying conjugategradient estimation to obtain the reduced parameter update vector as thesolution to the linear system.

In Example 27, the subject matter of Example 1 can optionally includefurther including generating a kernelized input signal vector byapplying a predefined mapping function to one or more elements of theinput signal vector, wherein the parameter vector describes asubstantially linear relationship between the kernelized input signalvector and a target signal component of the output signal vector.

In Example 28, the subject matter of Example 27 can optionally includewherein calculating the covariance matrix and the correlation vectorbased on the input signal vector and the output signal vector includescalculating the covariance matrix as the covariance matrix of thekernelized input signal vector and calculating the correlation vector asthe correlation vector between the kernelized input signal vector andthe output signal vector.

In Example 29, the subject matter of Example 1 can optionally includewherein processing the one or more signals associated with the inputsignal vector using the updated parameter vector includes generating amapped input signal vector based on the input signal vector, wherein theupdated parameter vector describes a linear relationship between themapped input signal vector and a target signal component associated withthe output signal vector, and applying the updated parameter vector tothe mapped input signal vector in order to estimate the target signalcomponent associated with the output signal vector.

In Example 30, the subject matter of Example 29 can optionally includewherein the input signal vector is based on one or more transmit signalspreviously transmitted by a transmit chain of a transceiver and theoutput signal vector is based on one or more receive signals previouslyreceived by a receive chain of the transceiver, and wherein the updatedparameter vector describes the linear relationship between the mappedinput signal vector and a signal leakage component contained in the oneor more receive signals.

Example 31 is a transceiver device. The transceiver device includes atransmit chain configured to transmit one or more transmit signals, areceive chain configured to receive one or more receive signals, and aprocessor configured to calculate a covariance matrix and a correlationvector based on the one or more transmit signals and the one or morereceive signals, identify a plurality of critical elements of aparameter vector based on a predefined criteria, wherein the parametervector represents a relationship between the one or more transmitsignals and the one or more receive signals, calculate a solution to alinear system to generate a reduced parameter update vector having aplurality of elements, wherein the linear system is based on theplurality of critical elements, the covariance matrix, and thecorrelation vector, update the parameter vector using the reducedparameter update vector to generate an updated parameter vector, whereinthe reduced parameter update vector has fewer elements than theparameter vector, and process at least one of the one or more transmitsignals using the updated parameter vector.

In Example 32, the subject matter of Example 31 can optionally includewherein the processor is configured to identify a plurality of criticalelements of a parameter vector by selecting a plurality of elements fromthe parameter vector as the plurality of critical elements, wherein thequantity of the plurality of critical elements is less than the quantityof elements of the parameter vector, and wherein processor is configuredto update the parameter vector using the reduced parameter update vectorto generate an updated parameter vector by updating only the pluralityof critical elements of the parameter vector.

In Example 33, the subject matter of Example 31 can optionally includewherein each of the plurality of critical elements of the parametervector corresponds to a respective element of the reduced parameterupdate vector, and wherein the processor is configured to update theparameter vector by updating only the plurality of critical elements ofthe parameter vector using the reduced parameter update vector togenerate the updated parameter vector.

In Example 34, the subject matter of Example 33 can optionally includewherein the processor is configured to identify the plurality ofcritical elements of the parameter vector based on the predefinedcriteria by generating a parameter remainder vector based on theparameter vector, the covariance matrix, and the correlation vector,identifying a predefined quantity of elements of the parameter remaindervector having the highest magnitudes according to the predefined rankingcriteria, and selecting the elements of the parameter vector thatcorrespond to the predefined quantity of elements of the parameterremainder vector as the plurality of critical elements of the parametervector.

In Example 35, the subject matter of Example 34 can optionally includewherein the processor is configured to select the predefined quantity ofelements of the parameter remainder vector to generate a reducedparameter remainder vector, wherein the reduced parameter remaindervector consists of the predefined quantity of elements of the parameterremainder vector.

In Example 36, the subject matter of Example 35 can optionally includewherein the processor is configured to select the elements of thecovariance matrix that correspond to the plurality of critical elementsof the parameter vector to generate a reduced covariance matrix.

In Example 37, the subject matter of Example 36 can optionally includewherein the linear system includes the reduced parameter remaindervector and the reduced covariance matrix and wherein the linear systemrepresents the linear relationship between the reduced parameterremainder vector and the reduced covariance matrix, and wherein theprocessor is configured to calculate the solution to the linear systemto generate the reduced parameter update vector by performing linearapproximation to obtain the reduced parameter update vector as thesolution to the linear system.

In Example 38, the subject matter of Example 37 can optionally includewherein the processor is configured perform linear approximation toobtain the reduced parameter update vector as the solution to the linearsystem by performing conjugate gradient estimation on the linear system.

In Example 39, the subject matter of Example 37 can optionally includewherein the processor is configured to update the parameter vector usingthe reduced parameter update vector to generate the updated parametervector by updating only the plurality of critical elements of theparameter vector using the reduced parameter update vector to generatethe updated parameter vector.

In Example 40, the subject matter of Example 34 can optionally includewherein processor is configured to generate the parameter remaindervector as a linear combination of the parameter vector, the covariancematrix, and the correlation vector.

In Example 41, the subject matter of any one of Examples 31 to 40 canoptionally include wherein the processor is configured to identify aplurality of critical elements of a parameter vector based on apredefined criteria by identifying a predefined quantity of elements ofthe parameter vector as a plurality of critical elements of theparameter vector.

In Example 42, the subject matter of any one of Examples 31 to 41 canoptionally include wherein the updated parameter vector estimates signalleakage between the transmit chain and the receive chain, and whereinthe processor is configured to process at least one of the one or moretransmit signals using the updated parameter vector by applying theupdated parameter vector to an input signal vector including the one ormore transmit signals to generate an estimated leakage signal, andapplying the estimated leakage signal to at least one of the one or morereceive signals in order to mitigate signal leakage from the at leastone of the one or more receive signals.

In Example 43, the subject matter of any one of Examples 31 to 42 canoptionally include wherein the processor is configured to calculate thesolution to the linear system to generate the reduced parameter updatedvector by applying conjugate gradient estimation to the linear system toobtain the reduced parameter update vector as a solution to the linearsystem.

In Example 44, the subject matter of any one of Examples 31 to 43 canoptionally include wherein the processor is further configured togenerate a kernelized input signal vector by applying a predefinedmapping function to at least one of the one or more transmit signals,wherein the parameter vector represents a linear relationship betweenthe kernelized input signal vector and signal leakage contained in theone or more receive signals.

In Example 45, the subject matter of Example 44 can optionally includewherein the processor is configured to generate a kernelized inputsignal vector by applying a non-linear predefined mapping function to atleast one of the one or more transmit signals.

In Example 46, the subject matter of Example 44 can optionally includewherein the processor is configured to calculate the covariance matrixand the correlation vector based on the one or more transmit signals andthe one or more receive signals by calculating the covariance matrix asthe covariance matrix of the kernelized input signal vector, andcalculating the correlation vector as the correlation vector between thekernelized input signal vector and an output signal vector including atleast one of the one or more receive signals.

Example 47 is a transceiver device. The transceiver device includes atransmit chain configured to transmit one or more transmit signals, areceive chain configured to receive one or more receive signals, and aprocessor configured to calculate a covariance matrix and a correlationvector based on the one or more transmit signals and the one or morereceive signals, identify a plurality of critical elements of aparameter vector based on a predefined criteria, wherein the parametervector describes a relationship between the one or more transmit signalsand the one or more receive signals, calculate a solution to a linearsystem using conjugate gradient estimation to generate a reducedparameter update vector having a plurality of elements, wherein thelinear system is based on the plurality of critical elements, thecovariance matrix, and the correlation vector, update the parametervector using the reduced parameter update vector to generate an updatedparameter vector, wherein the reduced parameter update vector has fewerelements than the parameter vector, and generate an estimated leakagesignal by applying the updated parameter vector to the one or moretransmit signals, and utilize the estimated leakage signal to cancel aleakage signal from at least one of the receive signals.

In Example 48, the subject matter of Example 47 can optionally includewherein the processor is configured to identify a plurality of criticalelements of a parameter vector based on predefined criteria by selectinga predefined quantity of critical elements of the plurality of criticalelements of the parameter vector.

In Example 49, the subject matter of Example, can optionally includeprocessor is configured to update the parameter vector using the reducedparameter update vector to generate an updated parameter vector byupdating only the plurality of critical elements of the parametervector.

In Example 50, the subject matter of Example 47 can optionally includewherein the processor is configured to update the parameter vector byupdating only the plurality of critical elements of the parameter vectorusing the reduced parameter update vector to generate the updatedparameter vector.

In Example 51, the subject matter of any one of Examples 47 to 50 canoptionally include wherein the processor is configured to generate theestimated leakage signal by calculating a mapped input signal vectorusing a new transmit signal of the one or more transmit signals, whereinthe parameter vector describes a substantially linear relationshipbetween the mapped input signal vector and signal leakage from thetransmit chain to the receive chain, and applying the updated parametervector to the mapped input signal vector to generate the estimatedleakage signal.

In Example 52, the subject matter of any one of Examples 47 to 51 canoptionally include wherein the processor is configured to identify theplurality of critical elements of the parameter vector by generating aparameter remainder vector based on the parameter vector, the covariancematrix, and the correlation vector, applying the predefined criteria tothe parameter remainder vector to identify a plurality of highest-rankedelements of the parameter remainder vector, and selecting the pluralityof critical elements of the parameter vector as the elements of theparameter vector that correspond to the plurality of highest-rankedelements of the parameter remainder vector.

In Example 53, the subject matter of Example 52 can optionally includewherein the predefined criteria is based on magnitude, and wherein theprocessor is configured to apply the predefined criteria to theparameter remainder vector to identify the plurality of highest-rankedelements of the parameter remainder vector by selecting a predefinedquantity of elements of the parameter remainder vector that have thehighest magnitudes as the plurality of highest-ranked elements of theparameter remainder vector.

In Example 54, the subject matter of Example 47 can optionally includewherein the processor is further configured to apply a predefinedmapping function to the one or more transmit signals to generate akernelized transmit signal vector, wherein the parameter vectordescribes a linear relationship between the one or more transmit signalsand signal leakage contained in the one or more receive signals.

In Example 55, the subject matter of Example 54 can optionally includewherein the processor is configured to apply a predefined mappingfunction to the one or more transmit signals to generate a kernelizedtransmit signal vector by applying a non-linear predefined mappingfunction to the one or more transmit signals.

In Example 56, the subject matter of Example 54 can optionally includewherein the processor is configured to calculate the covariance matrixand the correlation vector based on the one or more transmit signals andthe one or more receive signals by calculating the covariance matrix asthe covariance matrix of the kernelized transmit signal vector, andcalculating the correlation vector as the correlation vector between thekernelized transmit signal vector and a receive signal vector includingat least one of the one or more receive signals.

In Example 57, the subject matter of any one of Examples claims 47 to 56can optionally include wherein the processor is configured to identify aplurality of critical elements of a parameter vector based on apredefined criteria by selecting a predefined quantity of elements ofthe parameter vector as the plurality of critical elements of theparameter vector.

In Example 58, the subject matter of Example 47 can optionally includewherein the processor is configured to identify the plurality ofcritical elements of the parameter vector based on the predefinedcriteria by generating a parameter remainder vector by performing alinear operation on the parameter vector, the covariance matrix, and thecorrelation vector, identifying a predefined quantity of elements of theparameter remainder vector having the largest magnitudes according tothe predefined criteria, and identifying the elements of the parametervector that each correspond to a respective element of the predefinedquantity of elements of the parameter remainder vector as the pluralityof critical elements of the parameter vector.

In Example 59, the subject matter of Example 47 can optionally includewherein the processor is further configured to select the predefinedquantity of elements of the parameter remainder vector to generate areduced parameter remainder vector, and select a plurality of elementsof the covariance matrix corresponding to the plurality of criticalelements of the parameter vector to generate a reduced covariancematrix, wherein the linear system includes the reduced parameterremainder vector and the reduced covariance matrix.

In Example 60, the subject matter of Example 59 can optionally includewherein the linear system describes a linear relationship between thereduced parameter remainder vector and the reduced covariance matrix,and wherein the processor is configured to calculate the solution to thelinear system using conjugate gradient estimation to generate thereduced parameter update vector by performing conjugate gradientestimation on the linear system to obtain the reduced parameter updatevector as the solution to the linear system.

In Example 61, the subject matter of Example 59 can optionally includewherein the processor is configured to generate a reduced parameterremainder vector by selecting a predefined quantity of elements of theparameter remainder vector as the reduced parameter remainder vector.

In Example 62, the subject matter of any one of Examples 47 to 61 canoptionally include wherein the processor is configured to generate theestimated leakage signal by applying the updated parameter vector to theone or more transmit signals by applying the updated parameter vector toa transmit signal vector based on the one or more transmit signals togenerate the estimated leakage signal.

In Example 63, the subject matter of Example 62 can optionally includewherein the processor is further configured to generate the transmitsignal vector by applying a predefined mapping function to the one ormore transmit signals, wherein parameter vector describes asubstantially linear relationship between the transmit signal vector andthe leakage signal.

In Example 64, the subject matter of Example 47 can optionally includewherein processor is configured to utilize the estimated leakage signalto cancel a leakage signal from at least one of the receive signals byutilizing the leakage estimated leakage signal to cancel a leakagesignal arising from the transmit chain from at least one of the receivesignals.

While the invention has been particularly shown and described withreference to specific embodiments, it should be understood by thoseskilled in the art that various changes in form and detail may be madetherein without departing from the spirit and scope of the invention asdefined by the appended claims. The scope of the invention is thusindicated by the appended claims and all changes which come within themeaning and range of equivalency of the claims are therefore intended tobe embraced.

1. A method of processing signals comprising: calculating a covariancematrix and a correlation vector based on an input signal vector and anoutput signal vector; identifying a plurality of critical elements of aparameter vector based on a predefined criteria, wherein the parametervector represents a relationship between the input signal vector and theoutput signal vector; calculating a solution to a linear system togenerate a reduced parameter update vector having a plurality ofelements, wherein the linear system is based on the plurality ofcritical elements of the parameter vector, the covariance matrix, andthe correlation vector; updating the plurality of critical elements ofthe parameter vector using the reduced parameter update vector togenerate an updated parameter vector, wherein the reduced parameterupdate vector has less elements than the parameter vector; andprocessing one or more signals associated with the input signal vectorusing the updated parameter vector.
 2. The method of claim 1, whereinupdating the plurality of critical elements of the parameter vectorusing the reduced parameter update vector to generate an updatedparameter vector comprises: updating only the plurality of criticalelements of the parameter vector.
 3. The method of claim 1, furthercomprising: with a transmit chain of a transceiver, transmitting one ormore transmit signals; and with a receive chain of the transceiver,receiving one or more receive signals, wherein the input signal vectoris based on the one or more transmit signals and the output signalvector is based on the one or more receive signals.
 4. The method ofclaim 3, wherein processing the one or more signals associated with theinput signal vector using the updated parameter vector comprises:applying the updated parameter vector to a new input signal intended fortransmission by the transmit chain of the transceiver to generate anestimated leakage signal, wherein the estimated leakage approximatessignal leakage from the transmit chain to a the receive chain of thetransceiver; and utilizing the estimated leakage signal to cancel anactual leakage signal from a received signal received by the receivechain of the transceiver.
 5. The method of claim 4, wherein applying theupdated parameter vector to the new input signal intended fortransmission by the transmit chain of the transceiver to generate anestimated leakage signal comprises: updating the input signal vectorbased on the new input signal to generate an updated input signalvector; applying a mapping function to the updated input signal vectorto generate a kernelized input signal vector, where the parameter vectordescribes a linear relationship between the kernelized input signalvector and the signal leakage; and applying the updated parameter vectorto the kernelized input signal vector to generate the estimated leakagesignal.
 6. The method of claim 1, wherein identifying the plurality ofcritical elements of the parameter vector based on the predefinedcriteria comprises: generating a parameter remainder vector based on theparameter vector, the covariance matrix, and the correlation vector;applying the predefined criteria to the parameter remainder vector toidentify a plurality of highest-ranked elements of the parameterremainder vector; and selecting the elements of the parameter vectorthat each correspond to a respective element of the plurality ofhighest-ranked elements of the parameter remainder vector as theplurality of critical elements of the parameter vector.
 7. The method ofclaim 6, wherein the predefined criteria is based on magnitude, andwherein applying the predefined criteria to the parameter remaindervector to identify the plurality of highest-ranked elements of theparameter remainder vector comprises: selecting a predefined quantity ofelements of the parameter remainder vector that have thehighest-magnitudes as the plurality of highest-ranked elements of theparameter remainder vector.
 8. The method of claim 6, wherein the linearsystem describes a linear relationship between the reduced parameterremainder vector and a plurality of elements of the covariance matrixthat correspond with the elements of the reduced parameter remaindervector, and wherein calculating the solution to the linear system togenerate the reduced parameter update vector having less elements thanthe parameter vector comprises: applying conjugate gradient estimationto obtain the reduced parameter update vector as the solution to thelinear system.
 9. The method of claim 1, further comprising: generatinga kernelized input signal vector by applying a predefined mappingfunction to one or more elements of the input signal vector, wherein theparameter vector describes a substantially linear relationship betweenthe kernelized input signal vector and a target signal component of theoutput signal vector.
 10. The method of claim 9, wherein calculating thecovariance matrix and the correlation vector based on the input signalvector and the output signal vector comprises: calculating thecovariance matrix as the covariance matrix of the kernelized inputsignal vector and calculating the correlation vector as the correlationvector between the kernelized input signal vector and the output signalvector.
 11. A transceiver device comprising: a transmit chain configuredto transmit one or more transmit signals; a receive chain configured toreceive one or more receive signals; and a processor configured to:calculate a covariance matrix and a correlation vector based on the oneor more transmit signals and the one or more receive signals; identify aplurality of critical elements of a parameter vector based on apredefined criteria, wherein the parameter vector represents arelationship between the one or more transmit signals and the one ormore receive signals; calculate a solution to a linear system togenerate a reduced parameter update vector having a plurality ofelements, wherein the linear system is based on the plurality ofcritical elements, the covariance matrix, and the correlation vector;update the parameter vector using the reduced parameter update vector togenerate an updated parameter vector, wherein the reduced parameterupdate vector has fewer elements than the parameter vector; and processat least one of the one or more transmit signals using the updatedparameter vector.
 12. The transceiver device of claim 11, wherein eachof the plurality of critical elements of the parameter vectorcorresponds to a respective element of the reduced parameter updatevector, and wherein the processor is configured to update the parametervector by: updating only the plurality of critical elements of theparameter vector using the reduced parameter update vector to generatethe updated parameter vector.
 13. The transceiver device of claim 12,wherein the processor is configured to identify the plurality ofcritical elements of the parameter vector based on the predefinedcriteria by: generating a parameter remainder vector based on theparameter vector, the covariance matrix, and the correlation vector;identifying a predefined quantity of elements of the parameter remaindervector having the highest magnitudes according to the predefined rankingcriteria; and selecting the elements of the parameter vector thatcorrespond to the predefined quantity of elements of the parameterremainder vector as the plurality of critical elements of the parametervector.
 14. The transceiver device of claim 11, wherein the updatedparameter vector estimates signal leakage between the transmit chain andthe receive chain, and wherein the processor is configured to process atleast one of the one or more transmit signals using the updatedparameter vector by: applying the updated parameter vector to an inputsignal vector comprising the one or more transmit signals to generate anestimated leakage signal; and applying the estimated leakage signal toat least one of the one or more receive signals in order to mitigatesignal leakage from the at least one of the one or more receive signals.15. The transceiver device of claim 11, wherein the processor isconfigured to calculate the solution to the linear system to generatethe reduced parameter updated vector by: applying conjugate gradientestimation to the linear system to obtain the reduced parameter updatevector as a solution to the linear system.
 16. A transceiver devicecomprising: a transmit chain configured to transmit one or more transmitsignals; a receive chain configured to receive one or more receivesignals; and a processor configured to: calculate a covariance matrixand a correlation vector based on the one or more transmit signals andthe one or more receive signals; identify a plurality of criticalelements of a parameter vector based on a predefined criteria, whereinthe parameter vector describes a relationship between the one or moretransmit signals and the one or more receive signals; calculate asolution to a linear system using conjugate gradient estimation togenerate a reduced parameter update vector having a plurality ofelements, wherein the linear system is based on the plurality ofcritical elements, the covariance matrix, and the correlation vector;update the parameter vector using the reduced parameter update vector togenerate an updated parameter vector, wherein the reduced parameterupdate vector has fewer elements than the parameter vector; and generatean estimated leakage signal by applying the updated parameter vector tothe one or more transmit signals; and utilize the estimated leakagesignal to cancel a leakage signal from at least one of the receivesignals.
 17. The transceiver device of claim 16, wherein the processoris configured to update the parameter vector using the reduced parameterupdate vector to generate an updated parameter vector by: updating onlythe plurality of critical elements of the parameter vector.
 18. Thetransceiver device of claim 16, wherein the processor is configured togenerate the estimated leakage signal by: calculating a mapped inputsignal vector using a new transmit signal of the one or more transmitsignals, wherein the parameter vector describes a substantially linearrelationship between the mapped input signal vector and signal leakagefrom the transmit chain to the receive chain; and applying the updatedparameter vector to the mapped input signal vector to generate theestimated leakage signal.
 19. The transceiver device of claim 16,wherein the processor is configured to identify the plurality ofcritical elements of the parameter vector by: generating a parameterremainder vector based on the parameter vector, the covariance matrix,and the correlation vector; applying the predefined criteria to theparameter remainder vector to identify a plurality of highest-rankedelements of the parameter remainder vector; and selecting the pluralityof critical elements of the parameter vector as the elements of theparameter vector that correspond to the plurality of highest-rankedelements of the parameter remainder vector.
 20. The transceiver deviceof claim 19, wherein the predefined criteria is based on magnitude, andwherein the processor is configured to apply the predefined criteria tothe parameter remainder vector to identify the plurality ofhighest-ranked elements of the parameter remainder vector by: selectinga predefined quantity of elements of the parameter remainder vector thathave the highest magnitudes as the plurality of highest-ranked elementsof the parameter remainder vector.